Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration

Autores
Rigal, L.; Zadunaisky Bustillos, Pablo Mauricio
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the present paper, we are interested in natural quantum analogues of Richardson varieties in the type A grassmannians. To be more precise, the objects that we investigate are quantum analogues of the homogeneous coordinate rings of Richardson varieties which appear naturally in the theory of quantum groups. Our point of view, here, is geometric: we are interested in the regularity properties of these non-commutative varieties, such as their irreducibility, normality, Cohen–Macaulayness… in the spirit of non-commutative algebraic geometry. A major step in our approach is to show that these algebras have the structure of an algebra with a straightening law. From this, it follows that they degenerate to some quantum analogues of toric varieties.
Fil: Rigal, L.. Universite de Paris 13-Nord; Francia
Fil: Zadunaisky Bustillos, Pablo Mauricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
Algebra
Quantum
Flag
Schubert
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/19931
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/19931
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Quantum analogues of Richardson varieties in the grassmannian and their toric degenerationRigal, L.Zadunaisky Bustillos, Pablo MauricioAlgebraQuantumFlagSchuberthttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In the present paper, we are interested in natural quantum analogues of Richardson varieties in the type A grassmannians. To be more precise, the objects that we investigate are quantum analogues of the homogeneous coordinate rings of Richardson varieties which appear naturally in the theory of quantum groups. Our point of view, here, is geometric: we are interested in the regularity properties of these non-commutative varieties, such as their irreducibility, normality, Cohen–Macaulayness… in the spirit of non-commutative algebraic geometry. A major step in our approach is to show that these algebras have the structure of an algebra with a straightening law. From this, it follows that they degenerate to some quantum analogues of toric varieties.Fil: Rigal, L.. Universite de Paris 13-Nord; FranciaFil: Zadunaisky Bustillos, Pablo Mauricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaElsevier Inc2012-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19931Rigal, L.; Zadunaisky Bustillos, Pablo Mauricio; Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration; Elsevier Inc; Journal Of Algebra; 372; 12-2012; 293-3170021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2012.09.016info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0021869312004577info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1107.1396info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:12:09Zoai:ri.conicet.gov.ar:11336/19931instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-10 13:12:09.322CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
title Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
spellingShingle Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
Rigal, L.
Algebra
Quantum
Flag
Schubert
title_short Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
title_full Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
title_fullStr Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
title_full_unstemmed Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
title_sort Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
dc.creator.none.fl_str_mv Rigal, L.
Zadunaisky Bustillos, Pablo Mauricio
author Rigal, L.
author_facet Rigal, L.
Zadunaisky Bustillos, Pablo Mauricio
author_role author
author2 Zadunaisky Bustillos, Pablo Mauricio
author2_role author
dc.subject.none.fl_str_mv Algebra
Quantum
Flag
Schubert
topic Algebra
Quantum
Flag
Schubert
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In the present paper, we are interested in natural quantum analogues of Richardson varieties in the type A grassmannians. To be more precise, the objects that we investigate are quantum analogues of the homogeneous coordinate rings of Richardson varieties which appear naturally in the theory of quantum groups. Our point of view, here, is geometric: we are interested in the regularity properties of these non-commutative varieties, such as their irreducibility, normality, Cohen–Macaulayness… in the spirit of non-commutative algebraic geometry. A major step in our approach is to show that these algebras have the structure of an algebra with a straightening law. From this, it follows that they degenerate to some quantum analogues of toric varieties.
Fil: Rigal, L.. Universite de Paris 13-Nord; Francia
Fil: Zadunaisky Bustillos, Pablo Mauricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description In the present paper, we are interested in natural quantum analogues of Richardson varieties in the type A grassmannians. To be more precise, the objects that we investigate are quantum analogues of the homogeneous coordinate rings of Richardson varieties which appear naturally in the theory of quantum groups. Our point of view, here, is geometric: we are interested in the regularity properties of these non-commutative varieties, such as their irreducibility, normality, Cohen–Macaulayness… in the spirit of non-commutative algebraic geometry. A major step in our approach is to show that these algebras have the structure of an algebra with a straightening law. From this, it follows that they degenerate to some quantum analogues of toric varieties.
publishDate 2012
dc.date.none.fl_str_mv 2012-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/19931
Rigal, L.; Zadunaisky Bustillos, Pablo Mauricio; Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration; Elsevier Inc; Journal Of Algebra; 372; 12-2012; 293-317
0021-8693
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19931
identifier_str_mv Rigal, L.; Zadunaisky Bustillos, Pablo Mauricio; Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration; Elsevier Inc; Journal Of Algebra; 372; 12-2012; 293-317
0021-8693
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2012.09.016
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0021869312004577
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1107.1396
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Inc
publisher.none.fl_str_mv Elsevier Inc
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.993085

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